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HyCu (pronounce like Haiku)

Hyperelliptic curve counter implements counts points of hyperelliptic curves over finite fields.


HyCu is built using CMake, and provides four targets: single, threaded, mpi, and merger.

To build and install the threaded version HyCu with no further adjustments into PREFIX/bin use

cmake -D CMAKE_INSTALL_PREFIX=/home/martin/Documents/Mathematik/Projekte/hycu 

This assumes that the compiler is C++11 enabled by default. Prior GCC 6 you have to set the compiler flags

cmake -D CMAKE_CXX_FLAGS="-std=c++11" -D CMAKE_INSTALL_PREFIX=/home/martin/Documents/Mathematik/Projekte/hycu -D BuildThreaded=ON

CMake caches configuration variables, so you do not have to pass them again when you rebuild.

Check for available build options in CMakeList.txt.



We assume that HyCu is install in one of the PATHs.

To compute with a single curve over a prime field, for testing purposes mostly, you can use hycu-single.

hycu-single 7 3 2 6 8 2

If HyCu was compiled with OpenCL support, you can use it by passing the flag opencl.

hycu-single --opencl 3001 7 531 63 3 152 476 1002

If HyCu was compiled with timing support, timing results will be output.

Threaded and MPI

Threaded and MPI execution of HyCu is a two-step process. We generate unmerged data files in a result directory and then generate a single result file by

hycu-merger c result/q7g2 result/q7g2.hycu

This merges results for the path result/q7g2 into the file result/q7g2.hycu. The first option c is the store type, which currently must be c.

Running hycu on 2 threaded, using the configuration in config.yaml, and storing results into the path results:

hycu-threaded -n2 config.yaml results/

Running hycu with OpenMPI on 2 nodes with 16 threads each:

mpirun -n 2 --map-by ppr:1:node hycu-mpi -n 16 config.yaml results/

Skipping the number of threads lets HyCu use all available cores.

Configuration file

The config file is a YAML file. Its first entry may be

StoreType: EC

EC is the default value and stores results by ramification type, Hasse-Weil offsets, and curve count. It is currently the only value provided and thus you can skip this configuration option.

Sets of curves are described by the moduli section

  - Prime: 7
    PrimeExponent: 1
    Genus: 2
    ResultPath: q7g2
    PackageSize: 2500
  - Prime: 11
    PrimeExponent: 1
    Genus: 2
    ResultPath: q11g2
    PackageSize: 2500

Fields here should be most self-explanatory. The prime and prime exponent give the size of the base field. Currently, prime exponent 1 is the only one that is tested. Package size is a technical parameter, which should not be chosen too small. A reasonable size for many cases would be q^2 or q^3, where q is the base field size.

Store type EC

The results are stored as a text file with each line of the form:


The first numbers give the degree of factors of the right hand side. The next ones give the offset of the number of points to the Hasse-Weil average. After the colon the curve count is provided.


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